For the inequalities above, what is the maximum possible value of P +

Question

−2 < P ≤ −1

−1 < Q ≤ 0

0 < R ≤1

1 < S ≤ 2

For the inequalities above, what is the maximum possible value of P + Q + R + S ?

A. -2
B. 0
C. 2
D. 4
E. 6

CareerGeek · Answer

Maximum value = -1 + 0 + 1 + 2 = 2

IMO Option C

BrentGMATPrepNow · Answer

Since the inequality symbols are all facing in the  same direction , we can  add  them (piece-wise)

We get: (-2) + (-1) + 0 + 1 < P + Q + R + S ≤ (-1) + 0 + 1 + 2
Simplify to get: -2 < P + Q + R + S  ≤ 2

So the maximum value of the sum is  2

Answer: C

Cheers, 
Brent

nsdl1985 · Answer

Since R and S are +ve, maximize R and S. 
P and Q is either zero or negative, thus use value closer to zero or zero itself

thus
-1(P) + 0(Q) + 1(R) + 2(S)
=2

quisexplicabo · Answer

Why cant I do 0+0+1+2 =3 ?

Bunuel · Answer

Because we are given that  −2 < P ≤ −1 , so P cannot be 0, it can be at most -1.

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